Lower bound on the radii of circular orbits in the extremal Kerr black-hole spacetime

TL;DR

This paper investigates the radii of circular orbits around extremal Kerr black holes, providing evidence for a non-trivial lower bound related to the mass ratio of the black hole and orbiting particle.

Contribution

It introduces a lower bound on the radii of circular orbits in extremal Kerr spacetime based on the Thorne hoop conjecture, which was not previously established.

Findings

A non-trivial lower bound on orbit radii near extremal Kerr black holes.

The bound depends on the mass ratio of the black hole and orbiting particle.

Supports the idea that orbits cannot approach the horizon arbitrarily closely.

Abstract

It is often stated in the physics literature that maximally-spinning Kerr black-hole spacetimes are characterized by near-horizon co-rotating circular geodesics of radius $r_{\text{circular}}$ with the property $r_{\text{circular}}\to r^+_{\text{H}}$, where $r_{\text{H}}$ is the horizon radius of the extremal black hole. Based on the famous Thorne hoop conjecture, in the present compact paper we provide evidence for the existence of a non-trivial lower bound ${{r_{\text{circular}}-r_{\text{H}}}\over{r_{\text{H}}}}\gtrsim (\mu/M)^{1/2}$ on the radii of circular orbits in the extremal Kerr black-hole spacetime, where $\mu/M$ is the dimensionless mass ratio which characterizes the composed black-hole-orbiting-particle system.